It is the copy (text) of something that is being prepared for publishing before it is formatted for the print page. For example, if you were writing an article for a newspaper, it would be the article formatted (most likely) in a single column format. Soon your galley proof would be formatted into a several-column format typical of newspapers.

As mentioned - a galley is a term used in journalism to prepare pages before print. I don't believe a galley is used too much any more with the advent of computer-based layout programs like Quark Xpress.